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A216544 Decimal expansion of Sum_{k=1..500000} (-1)^(k-1)/(2k-1).

%I A216544 #24 Feb 04 2025 10:03:50
%S A216544 7,8,5,3,9,7,6,6,3,3,9,7,4,4,8,3,1,0,1,1,5,6,6,0,8,4,5,8,1,7,3,7,5,7,
%T A216544 2,1,0,4,9,3,2,2,8,4,9,8,4,3,7,7,5,7,6,2,7,4,3,7,3,6,1,7,3,3,3,7,4,5,
%U A216544 4,1,0,0,2,2,0,1,6,9,7,4,9,7,5,6,6,8,9,1,9,6,8,2,5,8,3,3,5,1,0,9,2,4,2,3,9,4,6,1,4,6,5,8,5,5,8,9,1,0,6,7,6,8,9,3
%N A216544 Decimal expansion of Sum_{k=1..500000} (-1)^(k-1)/(2k-1).
%C A216544 An approximation to Pi/4. The constant is rational, by definition (a product of finitely many rational numbers).
%H A216544 J. M. Borwein, P. B. Borwein and K. Dilcher, <a href="http://www.jstor.org/stable/2324715">Pi, Euler numbers and asymptotic expansions</a>, Amer. Math. Monthly, 96 (1989), 681-687.
%H A216544 J. M. Borwein and R. M. Corless, <a href="http://www.cecm.sfu.ca/~jborwein/sloane/sloane.html">Review of "An Encyclopedia of Integer Sequences" by N. J. A. Sloane and Simon Plouffe</a>, SIAM Review, 38 (1996), 333-337.
%H A216544 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>.
%e A216544 0.7853976633974483101156608458173757210493228498437757627437361733374541...
%p A216544 Digits:=300; M:=500000; add(evalf((-1)^(k-1)/(2*k-1)), k=1..M);
%t A216544 RealDigits[Sum[(-1)^(k-1)/(2k-1),{k,500000}],10,130][[1]] (* _Harvey P. Dale_, Sep 11 2024 *)
%Y A216544 Cf. A000796, A216542, A013706, A216543, A216544, A216545, A013705, A216546, A216547, A216548.
%Y A216544 Cf. also A195793.
%K A216544 nonn,cons,easy
%O A216544 0,1
%A A216544 _N. J. A. Sloane_, Sep 08 2012